Cables accessed by the site also reveal criticism of British military operations in Afghanistan and US shock at what the reports called the "rude behaviour" of Prince Andrew when abroad.
Mr King's comments were reportedly made to the US ambassador, but the timing and further details were not immediately available. The most recent of the leaked cables were said to be from February, when Mr Cameron and Mr Osborne were still in opposition.
Further details to be published over the next few days claim that US commanders, Afghan president Hamid Karzai and local officials in Helmand had criticised the British military for failure to impose security around the town of Sangin in southern Afghanistan. Britain has more than 9,500 troops in Afghanistan, the second largest contingent after the United States. Britain has lost 345 troops in the conflict - about a third of them in the Sangin area.
British troops handed responsibility for the area to US troops earlier this year.